I might not be as learned and scholarly as Archimedes, but I felt the same excitement of discovery. On my part, I discovered equation for interpreting Indian Standard Time.
I will try to explain. Suppose you are waiting for your friend and call him up to ask when he/she will be coming. “I will be there in 15-20 minutes” is the reply you get.
Here assume 15 is x and 20 is y.
Now the actual time taken for your friend to arrive would be =
y + 2(y-x)
= 20 + 2(20-15)
= 20 + 2(5)
= 30 minutes.
You can apply the same formula to 5-10 minutes, 30-40 minutes, 1-2 hours, etc. and see that it works perfectly.